A survey of nonprofit organizations showed that online fundraising has increased in the past year. Based on a random sample of50nonprofits, the mean one-time gift donation in the past year was $34 ,with a standard deviation of $8.Complete parts a and b below.a. Construct a 99 %confidence interval estimate for the population one-time gift donation. less than or equals?mu?less than or equals?(Type integers or decimals rounded to two decimal places as needed.)b. Interpret the interval constructed in (a).Choose the correct answer below.A.The quality improvement team can be 9999 %confident that the new population mean turnaround time is the midpoint of the confidence interval.B.The quality improvement team can be9999 %confident that the new population mean turnaround time is contained within the confidence interval.Your answer is correct.C.The quality improvement team can be completely sure that the new population mean turnaround time is the midpoint of the confidence interval.D.The quality improvement team can be completely sure that the new population mean turnaround time is contained within the confidence interval.

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AyBaba7 AyBaba7 · Answer 1 · 2020-03-27T03:23:28+01:00

Answer:

The 99% confidence interval for the population one-time gift donation

= (31.08, 36.92)

Option B is correct.

The quality improvement team can be 99% confident that the new population mean turnaround time is contained within the confidence interval.

Step-by-step explanation:

The concept of confidence interval is to get an interval that will contain the mean with a certain level of confidence.

Confidence interval = (Sample Mean) ± (Margin of Error)

Sample Mean = $34

Margin of Error = (Critical value) × (standard deviation of the distribution of sample means)

Critical value for 99% confidence interval = 2.58 (from the z-score tables)

(standard deviation of the distribution of sample means) = (standard deviation)/√n

where n = sample size = 50

(standard deviation of the distribution of sample means) = (8)/√50

(standard deviation of the distribution of sample means) = 1.13

Margin of Error = 2.58 × 1.13 = 2.92

Confidence interval = (Sample Mean) ± (Margin of Error)

Lower Limit of the confidence interval = (Sample Mean) - (Margin of error)

= 34 - 2.92 = $31.08

Upper limit of the confidence interval = (Sample mean) + (Margin of error)

= 34 + 2.92 = $36.92

The 99% confidence interval = (31.08, 36.92)

Hope this Helps!!!